I will be writing this at the rate of one year per chapter, starting from 1999.

inspiration for this format from: dadoctorwhofan's "what if doctor who wasn't axed in 1989" youtube series.

chapter 1
1999

after jazz 3 was declined by gathering of developers, epic continued the search for a publisher they looked at some of the big name ones and eventually made a deal with activision.
the game would start like so: once you started the game you would be in a non-intractable jazz2 like environment, in carrotus castle, suddenly devan teleports into the room through a portal, taking jazz's children with a gravity gun like device, the game switches to a cartoon cutscene, jazz jumps through the portal just before it closes, jazz is shown tumbleing through a swirling vortex, morphing from a cartoon hand drawn style to pre rendered 3D.
the game would then start as we see in the betas.

after playing through the game as we see in the public demo, you must return to the rocket launch pad and fly to other planets to play the rest of the game, this would use a smb3 like map to move from planet to planet. planets would include: diamondus, tubelectric, medivo, labrat, bloxonius, lenti, some new ones, etc.

the ps2 version would have splitscreen multiplayer, with up to 4 players, there would be no online multiplayer, on pc however, there would be online multiplayer, a level editor, and no splitscreen.

playable characters were jazz spaz and lori, custom characters would be given more customiseability then ever before, they could be given individual clothing fur styles colors, with no more simple re-colorings of the base characters. razz would also be in the game teaching you about how the game works, you would first meet him in the tutorial cave, with an icon of his face appearing on help text, there would be different icons on the textboxes based on who is talking.
it would look a bit like this:

a grappling hook mechanic would also be added.

the game was a large success, getting ratings of 4 to 4.5 out of 5, as there were some complaints about the complexity of the level editor, and various multiplayer bugs, along with battle being the only multiplayer mode, treasure hunt and CTF would soon be added by official patch however.
jazz 3 city would have been started near the end of the year.

Oh and add this to the story: DanZeal would copy-paste the UT map Facing words to JJ3 and it would be in the JJ3 CTF mappool yay

Though I wouldn't like Razz to be a playable character. He should be Jazz's instructions/tutorial guy. You know, 'use the jump button to jump, tap it again while in the air to do a double jump' that kind of stuff. Since he's an engineer Jazz would meet him at the very start of your version of the game (Rocket pad) and explain how to drive it and handle the map you mentioned.